THOR1: A tool for school timetabling

This system is the result of our previous work on the subject of school timetabling. It was designed to respond mainly to Portuguese schools from various educational levels. It consists of three main blocks; a graphical user interface; an automatic scheduler and a relational database. This system is now in use by more than 100 schools in Portugal with significant success (http://www.fmaismais.pt). 1 Implementation Framework School timetabling is a classical combinatorial optimization problem which is associated with a set of constraints. It consists of assigning a set of lessons to time slots within a time period (typically a week), satisfying a set of constraints of various kinds 3. The constraints that we have used are related to Portuguese schools and are the result of multiple discussions we had previously with people from several Portuguese schools. In Table 1 it can be seen a summary of the constraints we have considered in solving this problem. The main issue regarding the constraints is that each user can weigh each constraint with a particular value and in this way different schools may have different values to each constraint. A lesson is the teaching unit. It is characterized by the triple * * * , , T C S . Where * T is a subset of the teachers set, * C is a subset of the classes set and * S is a subset of the subjects set. Each lesson has a duration measured in time slots. There are two types of lessons: 1. Simple lesson. Where * 1 C = and * 1 S = . 2. Compound lesson. Where * 1 C ≥ and/or * 1 S ≥ . 1 In Portuguese THOR stands for Tabelas Horárias which can be roughly translated by timetabling charts. E. K. Burke, H. Rudová (Eds.): PATAT 2006, pp. 532–535. ISBN 80-210-3726-1. Constraint Description 0 C Number of time slots of lessons that aren’t yet scheduled 1,2 C Number of time slots of overlapped lessons (1-classes; 2-teachers) 3,4 C Number of time slots exceeding the maximum allowed per day (3-classes; 4-teachers) 5,6 C Number of time slots exceeding the maximum consecutive time slots allowed (5-classes; 6-teachers). 7,8,9 C Number of preferable time slots filled (7-classes; 8-teachers; 9-subjects). 10,11 C Number of idle time slots (10-classes; 11-teachers) 12 C Number of time slots of lessons without a room assigned. 13,14,15 C Number of time slots that are forbidden and are filled with lessons (13-classes; 14-teachers; 15-subjects) 16 C Total number of teaching days for teachers 17 C Number of repetitions of lessons of the same subject in the same class per day 18 C Number of time slots that doesn’t satisfy the predefined space between lessons. Table 1. Constraint set In general, a compound lesson means that we have several classes joined together to attend a certain subject or it means that a class can be subdivided into subgroups to attend special subjects, like laboratories, etc. It is associated with each subject the kind of room it must have, i.e., the resources that there must exist in the room for a lesson of that subject should happen. This software tool was designed to respond mainly to Portuguese schools from various educational levels. It is based on a modular implementation, and consists of three main blocks; a graphical user interface; an automatic scheduler and a relational database (Fig. 1). It was developed in C++ using an object oriented technique. It runs on Microsoft Windows  and the database is implemented in Microsoft Access. There were two main objectives with the development of this system: 1. It should be fairly easy to interact with it. 2. It would generate good timetables in an automatic way. The graphical user interface (GUI) consists of several forms where it is possible to enter the school data (i.e., teachers, rooms, classes, subjects), and also change the individual schedules. THOR: A Tool for School Timetabling 533